这篇论文戳破了“数据足够就能预测一切”的常见假设，做因果推断、反事实推理或世界模型研究的开发者会看到理论上的新边界——原来预测器天生缺失跨世界耦合信息，而WorldKernel给出了补全它的数学框架，值得细读。
论文发现一个反直觉的失败模式：即使有足够观测和干预数据，强预测器在识别反事实世界之间的耦合时也会崩溃为单点，而真实值是一个数据无法缩小的可接受区间。作者提出将世界模型建模为可接受世界上的正半定耦合核，其对角线是普通后验（预测器能恢复的），非对角线是跨世界耦合（预测器无法恢复的）。该耦合核可以被边界约束、通过逻辑结构收紧、并通过针对性约束学习来缩小差距。论文提供了完整的理论框架，并指出完全重建该核在Sly-Sun阈值以下是可处理的，以上则不可近似。
WorldKernel: A World Model is the Coupling Kernel of Admissible Possible Worlds
A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.